Experimental perspectives of atom photon-interactions: From fundamental tests to quantum simulations Jiří Minář Centre for Quantum Technologies National University of Singapore ICFP 2012 Kolymv(b,p?)ari, Greece

People Q Information, Q Optics group of Valerio Scarani Q Gases Benoît Grémaud Christian Miniatura David Wilkowski (Exp.)

Introduction Quantum communication: Device independent scenarios AMO: lasers + atoms → trapping, cooling, precision manipulation and measurements strong interaction at single particle level: quantum communication and many body level (quantum gases): quantum simulators Quantum communication: Device independent scenarios Quantum simulations: Artificial gauge fields for cold atoms

Device Independent Goal of q. communication – communicate q. information; what does this mean ? Example: Simulation of quantum statistics with competent students Measurement device (FREE choice of measurement) x x a Quantum system Y “Y “ a Outcome Measured statistics: yields (conditional) probability distribution, nothing quantum

Device Independent What about correlations ? Y x y b a x y b a “Y “ Quantum state The students cannot simulate this experiment, even if they have shared in advance some common strategy l. x y b a “Y “ “Y “

Device Independent Message: use the correlations → quantitative criterion: Bell test Y x y b a Classically, one can show, that with arbitrary local strategies while for quantum states All one needs is the probability distribution → no specific assumption about the physical system being used = Device Independent certification of “quantumness” Typical application: Quantum Key Distribution, . . . Acin, A. et al., PRL 230501 (2007), Pironio et al., Nature 464, 1021(2010) , Rabelo, R. et al., PRL 107, 050502 (2011)

Loopholes Not the end of the story: detection + locality loophole locality loophole requires spacelike separated measurements detection loophole requires a min. detector efficiency (one requires that the total statistics violate Bell inequality) detection efficiency if no detection, output = +1 in principle, one needs to close both loopholes in order to certify Device Independent “quantumess”.

Loopholes – what has been done Series of various Bell experiments: Photons polarization qubits, Aspect 1982 (locality loophole ) time-bin qubits, Tittel 1998 qutrits, Thew 2004 hyper-entanglement, Ceccareli 2009 etc.... Ions & others two ions, Matsukevich 2008 (detection loophole ) atom-photon entanglement, Moehring 2004 atomic ensemble-photon entanglement, Matsukevich 2005 SC qubits, Ansmann 2009 etc... In principle “just” a technological challenge; Now a race for the 1st closing of both loopholes at the same time => feasible experimental proposal matching current technologies Engineering of hybrid quantum states

Q state engineering Sometimes unfeasible states Threshold for Bell violation violation no violation Which of these states can be engineered? Asymmetric test: atom + photon → efficient detection on atomic side + propagation of the photon possible implementation using CQED Araújo, M. et al., arXiv:1112.1719

Experimental realization Reminder of Cavity QED The system is described by the Jaynes – Cummings Hamiltonian not exactly solvable (with inputs and outputs), but becomes so under the approximation , i.e. atom in the ground state (this is what we want!) cavity acts as a linear filter with transmission dependent on the atomic state: coherent state remains coherent !

Experimental realization Reminder of Cavity QED better picture of the situation looking at the cavity transmission Transmission transmission in s channel ≠ transmission in g channel

Experimental realization Back to the state preparation using the cavity, one gets we want to bring this to zero: easy for coherent states – displacement using a beam splitter + one traces out the “environmental modes” the final visibility does not depend on the details of the laser spectrum in principle one can get the state in the limit , Teo, C. et al., arXiv:1206.0074

Experimental realization Check the validity – the atom has to be in the ground state! yellow – good red – bad long pulse limit short pulse limit Teo, C. et al., arXiv:1206.0074

Experimental realization Implementations (what experimentalists need and like) Example of 87Rb (used in number of cavity experiments) identify the relevant levels, use (polarization) selection rules Teo, C. et al., arXiv:1206.0074

Performance Implementations (what experimentalists need and like) Example of 87Rb (used in number of cavity experiments) propagation distance available parameters Possible implementations in circuit QED ? (Fast operations – short propagation distances (~ 10 m) vs. problems with detection and transmission) Teo, C. et al., arXiv:1206.0074

Conclusion I Bell tests are essential in Device Independent applications Hybrid atom-photon entangled states are particularly interesting What other kind of states is one able to produce ?

Artificial gauge fields with cold atoms excellent platforms for simulating various physical phenomena why cold? → quantum degeneracy (BEC, …) high tunability – scattering length (via Feshbach resonances), various atomic species (bosons, fermions), lattice/bulk configurations, one can tune the dimensionality one “problem” – they’re neutral → artificial gauge fields

Artificial gauge fields with cold atoms Bulk Idea: Dress the internal atomic states with laser light acts on the internal states acts on center of mass U given by the laser field → the atom is dressed in the new eigenbasis of U Assuming adiabatic evolution of the atom initially in the state , one obtains the equation of motion of the center of mass of the atom vector potential scalar potential → Emergence of geometric gauge potentials Dalibard et. al, Rev. Mod. Phys. 83, 1523 (2011)

Artificial gauge fields with cold atoms Bulk Yes Experimental realization? Recipe for the vector potential: BEC of 87Rb + Raman laser coupling F=1 ground state manifold + spatially variable (2-photon) detuning (achieved by a gradient of a true magnetic field) Experimental signature → vortices

Artificial gauge fields with cold atoms Bulk So far Abelian gauge fields: Generalization to non-Abelian gauge fields using multiple levels Hamiltonian in the subspace of q degenerate states . . . . q x q matrices Non abelian potentials Yes Experimental realization? But only with specific form of the potentials allowed by the simple implementation – spin orbit coupling Lin, Y.-J. et al., Nature 471, 83 (2011), Chen, S. et al., Arxiv:1201.6018

Artificial gauge fields with cold atoms Lattice key element: hopping Interaction (on-site) t j j+1

Artificial gauge fields with cold atoms Lattice Raman coupling assisted hopping Interaction (on-site) emergence of effective Abelian gauge field j j+1 Yes Experimental realization?

Artificial gauge fields with cold atoms Lattice Raman coupling assisted hopping Interaction (on-site) N component spinor j j+1 emergence of effective non Abelian gauge field ? Experimental realization? Osterloh, K. et al., PRL 95, 010403 (2005)

Conclusion II So far only external gauge fields (given by the laser configuration) Proposals of dynamical gauge fields (lattice and bulk) U(1) → work in progress U(N>1) ??? Exciting future of simulations of quantum many body systems with artificial gauge fields Outlook

Thank You !